Yeah, it doesn't seem like there's any storage as far as I can tell.
One strategy that might help is combining the base ingredients into a more complex ingredient. So take that regular leather and make it into hardened leather. 3 weight turns into 1.
I definitely think they should consider reducing the weight of some of the materials since there is no storage.
In the meantime, avoid picking up leather, cloth, iron ore, and timber that's easily accessible in town if you are too low on inventory space.